Last Action Hero refers to real movies?

It is not so much a reference to a single particular movie, but to all the archetypical action movies of that kind, starring a hard-boiled one-man hero (usually a cop) who has a meaty name (like John McLane, Jericho Jackson, Jack Slater) and kills bad-guys while giving cool one-liners.

So no, it wasn't refering to an actual movie starring an actual Jack Slater, and yes, it was refering to a whole bunch (or whole genre) of other movies.

Believe it or not, the movie was actually inspired by The Simpsons. Yes, it's true. The movie's original writers, Zak Penn and Adam Leff, were quoted as saying,

The weird thing is that The Simpsons inspired it in the first place. We thought, ‘if this show can destroy genres even as it embraces them, why can’t we do it in live action?’

The lead, Jack Slater, was originally named Arno Slater, in a direct reference to Schwarzenegger, who ironically took the role. And there were other ironies too. Penn and Leff spent days studying Shane Black's scripts (particularly the Lethal Weapon movies and The Last Boy Scout) to get the satire just right, and Black was eventually hired to re-write the script. Additionally, they used Die Hard and other movies directed by John McTiernan to get the proper pacing, and then McTiernan was hired to direct it. Lastly, their villain was patterned after Alan Rickman's character in Die Hard, but after Rickman refused the role they specifically chose Charles Dance because of his resemblance to Rickman.

So, to specifically answer your question; No, it was not written about any previous character named Jack Slater, but was rather intended to mock the entire genre of over-the-top Action movies.

One last tidbit of irony, and likely just a strange coincidence, is that there was a real actor named Jack Slater, whose first movie role was playing a man named John Reese. John Connor. Kyle Reese. Terminator. Coincidence? You decide... ;-)